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anonymous
 one year ago
I need help understanding integration by substitution: 63/(9x+2)^8
anonymous
 one year ago
I need help understanding integration by substitution: 63/(9x+2)^8

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phi
 one year ago
Best ResponseYou've already chosen the best response.1if you let u = 9x+2 what is du ?

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1This is the as saying f(x) =9x+2 What is f'(x) Just a difference of differentials but you don't need to worry about thst

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1Yes just one thing you missed Du=9dx

phi
 one year ago
Best ResponseYou've already chosen the best response.1no du/dx =9 but if you "take the derivative" u= 9x you differentiate the variables, in this case the u and the x like this du = 9 dx

phi
 one year ago
Best ResponseYou've already chosen the best response.1and once you have du = 9 dx then you also have \[ dx = \frac{1}{9} du \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1now do your variable substitution replace 9x+2 with u replace dx with 1/9 du

phi
 one year ago
Best ResponseYou've already chosen the best response.1and if we have limits, we would also change the limits.

phi
 one year ago
Best ResponseYou've already chosen the best response.1and because it is easy to integrate a power, I would use the 8 exponent and get rid of the fraction

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So would it be: \[63u ^{8}*1/9 du\] ??

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes and the problem is \[ 7 \int u^{8} du \] which you can do , right?

phi
 one year ago
Best ResponseYou've already chosen the best response.1once you integrate, replace u with 9x+2 to put the answer in terms of x

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{63}{(9x+2)^8}~dx}\) \(\large\color{slate}{\displaystyle u=9x+2}\) \(\large\color{slate}{\displaystyle du=(9x+2)'~\cdot dx~~~\rightarrow~~~du=9~dx}\) (you already have a 9 and dx to replace that by du, just need to rewrite it. \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{7\cdot 9}{(9x+2)^8}~dx}\) \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{7}{(9x+2)^8}~(9\cdot dx)}\) substitution:: \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}\frac{7}{(u)^8}~(du)}\) and then all you have left:: \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}7~u^{8}~du}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(APPLY THE POWER RULE, AND don't forget to substitute the x back for u.)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, I got it! Thank you all!
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